# A Common Root

Algebra Level 3

There are three real values of b for which the equations:

$$2{ x }^{ 2 }+5x+2b=0$$ and $$2{ x }^{ 3 }+7{ x }^{ 2 }+5{ x }+1=0$$ have at least one common root.

The sum of these three values for b can be expressed in the form $$\frac { m }{ n }$$, where m and n are coprime positive integers.

Find $$m+n$$.

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